Question

1. this hanger containing 2 pentagons and 6 circles is in balance. use the hanger diagram to create two additional hangers that would be in balance.

Explanation:

Step1: Divide both sides by 2

If we assume the weight of a pentagon is \(p\) and the weight of a circle is \(c\), we have \(2p + 6c\) in balance. Dividing each side of the balance - equation by 2 gives \(p+3c\). So one balanced hanger could have 1 pentagon and 3 circles.

Step2: Multiply both sides by 2

Multiplying the original balance - equation \(2p + 6c\) by 2 gives \(4p + 12c\). So another balanced hanger could have 4 pentagons and 12 circles.

Answer:

1. A hanger with 1 pentagon and 3 circles.
2. A hanger with 4 pentagons and 12 circles.